are the left invariant vector fields which generate the horizontal distribution in \(\mathbb {H}\) . By a classical result of Folland [1]}, see also [2]}, the fundamental solution of \(\Delta _{\mathbb {H}}\)  is \(\Vert \cdot \Vert _{\mathrm {Kor}}^{-2}\)  where \(\Vert \cdot \Vert \)  is the Koranyi norm in \(\mathbb {H}\) . One then defines the Heisenberg Riesz kernel in \(\mathbb {H}\)  as
\( \mathsf {R}(x):=\frac{\nabla _{\mathbb {H}} \Vert x\Vert _{\mathrm {Kor}}^{-2}}{2}= \left( \frac{x (x^2+y^2)-4yz}{\Vert v\Vert _{\mathrm {Kor}}^6}, \frac{y(x^2+y^2)+4xz}{\Vert v\Vert _{\mathrm {Kor}}^6} \right),\) 
